I am interested in the history of the ordered pair.
When did ordered pairs as a concrete object, not necessarily defined in terms of sets, appear in a mathematical or logical setting?
The definition of ordered pairs in terms of sets goes back to Norbert Wiener with $\{\{\{a\}, \varnothing\}, \{\{b\}\}\}$, although Kuratowski's definition $\{\{a\}, \{a, b\}\}$ later superseded it.
It also appears that Principia Mathematica contained some form of ordered pair, perhaps as a primitive object or perhaps defined in terms of relations. (I actually can't tell based on the Wikipedia article.)
This answer on the philosophy stack exchange, however, explains that ordered pairs were used a long time ago to extend the expressive power of Aristotlean logic.
These devices have early traditional precursors, see Hodges, Traditional Logic, Modern Logic and Natural Language. E.g. Alexander of Aphrodisias and Ibn-Sina converted binary relational inferences into syllogisms by changing the domain of discourse to pairs.
As a brief, massively ahistorical aside, with two relations $A(p, x)$ and $B(p, y)$ defining projections out of a pair $p$ to $x$ and $y$ respectively we can build ordered pairs and then on to finite tuples of the form $(a_1, (a_2, a_3))$ or such. So a system that can handle binary relations could in principle be as expressive as first order logic.
It's not clear to me, though, whether Ibn Sina would have had an explicit concept of an ordered pair or not. This account of Ibn Sina's extension to Aristotlean logic may be ahistorical (it's possible that he used binary predicates but not ordered pairs).
If he did, I also don't know whether this would be the first usage of an ordered pair.
